Sword and sorcery setting (I understand Spelljammer? and Ravenloft may be exceptions)

technology no further advanced than the middle ages/renaissance

Usually, dungeon dives are involved, but the fun adventures don't use dungeons at all (at least in my experience).

From Level 1 until about level 5 or so, all characters are an unlucky sneeze away from death (most other games have the character a bit more resilient on the power-scale prior to starting play)

Power progression is not similar between classes. The fighter is overpowered (comparatively) at low levels, everyone kind of hits their stride somewhere around 5-10th levels, and after that, the mage overpowers the campaign, and Lord MacGuffin the brave fighter is reduced to the mage's bodyguard. Followers can change that, but most games I've been in have had the "no followers" rule (in addition to having to build a strong hold to attract red-shirts, and that can't be done if you are constantly on the road).

"Kill them and take their boots" - most other RPGs only do this inasmuch as they've inherited it from D&D. Killing enemies is common, searching them for intel or even loose money is somewhat common, stripping them of everything with a sale price is basically D&D and Warhammer only.

"That's Against My Alignment" - alignment has had a corrosive effect on D&D as it is commonly interpreted as prescriptive instead of descriptive. People are comfortable saying you should or must do something based on alignment (this has somewhat expanded to class and especially 4e role like "striker"). It is very rare in other games.

I think the one thing that's gone through each edition is that you'll be facing some fantastical creatures, usually in combat. Interesting creatures have always been a strength of D&D compared to other systems, with Earthdawn really being the only one to match, and in a similar vein the TV series Supernatural also brings up some very interesting creatures to face.

Another thing is specialised characters - people who are largely good at one thing. Obviously classes like the bard, and multiclassing dilute this characteristic, but they could also be used as an example of 'the exception proves the rule.' I think the efforts to make 3.5 classes more playable through all levels, rather than grabbing a level of Ranger and Barbarian each and doing the rest as Fighter shows a desire to keep specialist characters rather than generalist. Generalist characters are also usually quite ineffective in later editions, with perhaps 2nd Edition being the most open to them.

What are the core tropes and assumptions that players bring to a game
of D&D?

Specifically the ones that are different from other role-playing
games.

OK, I'll bite. I have the background, though I hate coming to these damn questions late.
Though I doubt I am answering in the way you want. Many of the expectaions and core assumptions do change by edition; despite this not being the intention of the designers. They are written for different game experiences, whether they realized it or not.

Some things that do not change?

Teamwork and role driven system and play.

Tolkienese races and structure.

'Human centric' system where humans are the great adaptor.

simplistic 'patron deity vs religion' religeous paradign

Moral alignment system

Medievalesque setting, despite the presence of magic.

Heroic to ultraheroic gameplay.

Divine vs arcane casting

However...

"RPGs are written with a play style and a setting style they are optimized for. When we talk about class or role balance, we are talking about the the critical rules fulcrum; where did the designers balance the game and how broad is that fulcrum?
I have spent time in other forums describing this from the point of design for 5e. For 4e, my translation of many of the earlier explanations is that they moved the fulcrum of player-role balance to combat. The 4e rules were actually very well done in accomplishing what they wanted to do. They just moved the fulcrum from where it used to be to combat.
Earlier versions of the game had role balance based mainly on exploration, and then later on the fulcrum moved over from pure exploration, to a bit of a widening of the fulcrum adding the longer adventure then adding the campaign to the fulcrum, with more and more emphasis being put on balancing the game in the long-term campaign. (you really have to look at the experience charts, stronghold building, tithes, men at arms and taxes, as well as the RAW with spell components in the older books to relly get a handle on the care that was put inot this balance)
4e's biggest difference, in my estimation, is making a radical change to the fulcrum of rules balance to combat. I have heard others make the same comment about it being an 'encounter-centric' game, but one needs to see where it changed from to understand how radical the change. Striker? Defender? It was obvious from the first that the role balance had shifted this way. In earler games, you accepted that your thief was going to shoot a lot of arrows and be second class in combat; but if you were smart and had a good GM, you were climbing walls, or hiding and scouting alot; or using your in-town abilities like picking pockets, and you had areas of you own you excelled in. the same was true in every class. yes, every notes that a high-level mage is a tougher opponent in earlier games, but they get their stronghold much later, it's a lot smaller and provides less revenue....all part of where rules balanced the game.
Or, if you prefer, as viewed from a different lens; it went from being a game whose rules-fulcrum was in an area where a cpg could not match to a fulcrum where the tabletop game had a severe visceral disadvantage to a MMORPG."

This was written in a different place, and for a different audience, but it serves to illustrate the point, that the rulese do are ade for different games. This is not an edition bash; this is merely the preable to the fact that some of the 'core tropes' are edition specific.

0D&D was written and balanced around the ideal of exploration as the prime game, dungeoning. The classes/roles were balanced upon this, so this was the game built for the delve, and later, with the addition of the first supplements, added the outdoor adventure to this...But this was the era of the DUNGEON part of dungeons and dragons ruling.

AD&D was written for the full campaign, and balanced that way. One has to look at the experience charts and the keeps and freeholds and tax revenues and tithes and more to really understand this...but this was a game built for HUMANS to rule the world, and for their abiity to keep advancing onward.
Evil was much more of an option here for players and the more refnined alignment system was part of the trope...

AS the newer editions, more of the balance started moving to combat; though skills balanced this a little bit. Things were getting more and more epic as time went on, and 4e continued this with paragon and epic tiers.
One big change was the trope of the heroic long-term weak-to powerful gameplay, which changed to 'hero to epic-level' as the editions moved onward.

these are D&D specific tropes and some basic edition changes that have changed with the editions. Hope this brings a useful perspective.

One core assumption (in D&D4 especially, but also to a lesser extent in 3.5 and before) is that the player characters are heroes. This means they're just better than ordinary inhabitants of the world - they get better ability scores, better character classes, etc. If you want to run a game where the players are just regular guys, D&D may not support it as well as some other systems, because "regular guys" in D&D are kinda boring.

Only for 4E. Under AD&D and Moldvay/Mentzer/Alston/Denning D&Ds, it would usually be a series of grind down encounters. Even under 3.5, it could be several set-piece combats. 4E slowed combat a good bit.
–
aramisMar 11 '11 at 3:46

In my answer I am deliberately ignoring D&D specific term and phrases and am focusing on external elements that are being brought to the table. Since D&D came first it has had a very large impact on how people approach RPGs in all forms.

It use to be back in the day the majority of gamers brought 1 or more of 5 main assumptions to the gaming table:
1. Tolkien
2. Lovecraft
3. Favorite book series (Fantasy/Sci-Fantasy)
4. Brothers Grimm or
5. the Dark Ages.

Today it seems that more gamers are coming to the table with a World of Warcraft or other similar digital fantasy environment firmly planted in their minds. Also some are very focused on one or more fantasy movie/TV themes.

Additionally, I see a trend towards impatience, (read this as meaning time lose intolerance). When I started back in the 70s, everyone spent hours pouring over the books gleaning bits of info here and there to tweak our characters. We thought nothing of spending many hours generating a single character. Today I can generate a whole party of characters in 15 minutes flat.

One of the assumptions by players coming in today is the "quick character builder" mentality. Many people complain about D&D tools but if you look around there are more of them specifically targeted at D&D than any other system.

I use to never get the question from my players - How do I use Grimm the barbarian? I used to get long speeches on Grimm's back story and why it should affect play so much. Today, character back story is a selection, and more often than not a player needs a little more coaching into who and what their character is.

I do not believe the reason for this is that today's player's are bad RPG'ers. In many ways today's players are even better than back in the day. What I believe is really happening is the lose of the time investment for a character to grow into the mind of the player before they ever roll their first initiative die.

As I re-read my answer here something jumps out to me. The first section is all about non-digital influences (tropes and assumptions) and the late section is primarily digitally oriented.

This is what I would think if someone offered to run a D&D game, or Forgotten Realms or Eberron for that matter, as contrasted with freeform fantasy game, Burning Wheel, Runequest, homebrewed fantasy game, Bliaron or the Shadow of Yesterday / World of Near (all more or as common than D&D, hereabouts). By my estimation, if someone were to run for example a Planescape game, they'd mention that primarily and then specify which rules they are using. So I'm assuming someone tells they are running a D&D game.

This all just to say that my response is very particular to the slice of gaming culture among university students in Jyväskylä with whom I have contact - probably completely different elsewhere.

Setting

Very high and mundane magic. There's magical stuff everywhere, but it often replaces mundane technology. In older D&D, there's magic stuff in the dungeons, at least, but maybe not outside them. In either case, magical items are commonplace and not wondrous, and monsters and mythical creatures likewise.

There are dungeons. Characters may actually seriously consider going in them with the expectation that there'll be treasures and lots of monsters there.

Late medieval trappings, but fundamentally modern setting. The values and behaviours of people are often very modern and liberal. Magic as technology may be involved in this, as well.

Many different divine beings worshipped, but most characters devoted to only one of them. Divine being enable some of their worshippers to cast divine spells (as opposed to, say, rare miracles or permanent blessings or whatever), which don't vary much or at all depending on the particular divinity.

Style of play

Player characters form a party that goes on adventures.

The adventures involve much fighting.

Old editions: Ten foot poles, very careful and strategic approach to dungeon crawling, high potential or actual character mortality, player ingenuity appreciated and left room for.

Newer editions: Heroic characters, often character optimisation and lots of mechanical engagement with an intricate game system, large potential for railroading, very long combats (as measured in playing time), most everything is ultimate solved by fighting something somewhere, low character mortality or new characters at almost party level.

Fast mechanical development of characters, and increased power in fiction, also.

Participant attitude

Participants do not generally take the fiction that seriously: Tongue-in-cheek, nostalgic return to childhood, thin veneer around the strategic/tactical play, or a reason to chat and meet friends.

If the GM takes it seriously, then railroading, non-standard setting or young GM.